Non-Hermitian quantum dynamics and entanglement of coupled nonlinear resonators

Abstract

-We consider a generalization of recently proposed non-Hermitian model for resonant cavities coupled by a chiral mirror by taking into account number non-conservation and nonlinear interactions. We analyze non-Hermitian quantum dynamics of populations and entanglement of the cavity modes. We find that an interplay of initial coherence and non-Hermitian coupling leads to a counterintuitive population transfer. While an initially coherent cavity mode is depleted, the other empty cavity can be populated more or less than the initially filled one. Moreover, presence of nonlinearity yields population collapse and revival as well as bipartite entanglement of the cavity modes. In addition to coupled cavities, we point out that similar models can be found in PT symmetric Bose-Hubbard dimers of Bose-Einstein condensates or in coupled soliton-plasmon waveguides. We specifically illustrate quantum dynamics of populations and entanglement in a heuristic model that we propose for a soliton-plasmon system with soliton amplitude dependent asymmetric interaction. Degree of asymmetry, nonlinearity and coherence are examined to control plasmon excitations and soliton-plasmon entanglement. Relations to PT symmetric lasers and Jahn-Teller systems are pointed out.Introduction. -Recently, an intriguing quantum optical model for resonant cavities coupled by a chiral mirror has been proposed [1]. The chiral mirror is a planar metamaterial array of asymmetric split rings, through which transmission of circularly polarized electromagnetic waves becomes different in the opposite direction without violating Lorentz reciprocity principle [2]. The transmission matrix of such a mirror is a two dimensional non-Hermitian matrix. The proposed quantum optical system is then described by a non-Hermitian Hamiltonian. As a special class of non-Hermitian systems, parity-time (PT ) symmetric systems have been attracted much attention [3][4][5]. More recently, it is shown that hybridized metamaterials can simulate effectively spontaneous symmetry breaking in PT -symmetric non-Hermitian quantum systems [6]. Nonreciprocal light transmission in PT -symmetry broken phase using whispering-gallery microcavities has been observed very recently [7].

Embedding quantum systems with a non-conserved probability in classical environments

“…The theoretical investigations are also undergoing rapid developments: non-Hermitian quantum mechanics has been investigated within a relativistic framework [31] and it has been adopted by various researchers as a means to describe open quantum systems [32][33][34][35][36][37][38][39][40][41][42]. Moreover, it seems that a few theoretical studies have been dedicated to the statistical mechanics and dynamics of systems with non-Hermitian Hamiltonians [43][44][45][46][47][48][49][50][51][52][53][54].…”

Dynamics of mode entanglement in a system of cavities coupled with a chiral mirror

“…Furthermore, the relations between mode correlations and the spin noise in coupled cavity systems have been revealed only recently [31]. The absence of bipartite mode entanglement * Electronic address: ahardal@ku.edu.tr due to the lack of nonlinearity in the model system under consideration has also been verified [6]. Here, we report the existence of genuine mode entanglement in the generic model that are robust and controllable via the asymmetry in the coupling of the two modes.…”

“…The dynamical analysis by the usual Heisenberg approach has revealed the asymmetric photon exchange between the resonators. In addition, the non-conservation of the total photon number was reported for the same model by employing the non-Hermitian quantum evolution [6]. The non-conservation of the mean number of photons is an interplay between the quantum coherence and the non-Hermitian dynamics.…”

“…The time evolution of a state ρ(t) of the system can be determined by the modified Liouville-von Neumann master equation [6] ∂ ∂t…”

Non-Hermitian interaction of a discrete state with a continuum

“…In particular, non-Hermitian couplings have been used to describe a PT -symmetric extension of the Lee model in the ghost regime 59,78,79 , non-Hermitian Bose-Hubbard Hamiltonians 80 , and PT -symmetric extensions of the Jaynes-Cumming model 81 . Effective models that yield non-Hermitian couplings are also encountered in the theory of the inverted quantum oscillators and quantum amplifiers 82,83 and introduced in several other systems 84,85,86,87,88,89,90,91 . In particular, engineered optical structures where photonic transport arises from evanescent field coupling can be tailored to simulate an effective non-Hermitian interaction between a discrete state (such as an optical resonator or waveguide) with a continuum of states (such as a chain of optical resonators, a waveguide array, a slab waveguide or a photonic crystal) 92,93 .…”